Simplest radical form — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
No perfect square factors left under the root.
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Perfect square — A number that is some whole number squared: 1, 4, 9, 16, 25, …
- Factor — A number that divides evenly into another.
Practise this idea
6 questions in the course bank use Simplest radical form, in Distance on the Coordinate Plane, Right Triangle Trigonometry, Equations of Circles, Coordinate Geometry Proofs.
Problem 1
Find the exact distance between (0, 0) and (5, 5), in simplest radical form.
Worked answer
5sqrt(2)
25 + 25 = 50
√50 = √25 · 2
= 5√2
Problem 2
A quadrilateral has vertices (0,0), (4,0), (4,4), (0,4). Find the length of a diagonal in simplest radical form.
Worked answer
4sqrt(2)
From (0,0) to (4,4)
16 + 16 = 32
√32 = 4√2
Problem 3
In a 45-45-90 triangle each leg is 7. Find the hypotenuse in simplest radical form.
Worked answer
7sqrt(2)
Hypotenuse = 7√2
Problem 4
In a 30-60-90 triangle the hypotenuse is 14. Find the longer leg in simplest radical form.
Worked answer
7sqrt(3)
Short leg = 7
Long leg = 7√3
Problem 5
Give the radius of (x-1)2 + (y+6)2 = 50 in simplest radical form.
Worked answer
5sqrt(2)
√50 = √25 · 2
= 5√2
Problem 6
Find the exact length from (-3,4) to (2,-1) in simplest radical form.
Worked answer
5sqrt(2)
√25+25 = √50
= 5√2